As image forming apparatuses such as printers, facsimile apparatuses, copying apparatuses and composite (or multi-function) apparatuses having the functions of the printer, facsimile apparatus and copying apparatus, there are the so-called ink-jet recording apparatuses which use an ink-jet recording head, for example. The ink-jet recording apparatus makes an image formation on a recording medium by ejecting ink from the ink-jet recording head onto the recording medium. The recording medium may be paper, OHP film or any suitable recording sheet onto which the ink may be adhered. The image formation includes various kinds of recording and printing of characters, images and/or photographs.
In such an ink-jet recording apparatus, increasing the resolution is one element for increasing the picture quality of the image that is formed on the recording medium. A pitch of nozzles of the recording head that ejects the ink may be reduced in order to obtain a high resolution. However, since there is a physical limit to reducing the nozzle pitch, the so-called interlace scanning is carried out so as to obtain a resolution that is an integer multiple of the nozzle pitch, with the sub scanning (or recording sheet feeding) accuracy and the impact dot diameter permitting.
Increasing the operation speed (or recording speed) of the ink-jet recording apparatus is another important element besides increasing the picture quality. Particularly in the case of a serial scan type image forming apparatus in which the recording head scans in a main scanning direction and the recording sheet is fed in a sub scanning direction, it is possible to achieve a recording speed that is approximately two times that of a one-way recording, by carrying out a two-way recording (or bi-directional recording) which ejects the ink onto the recording sheet during both a forward path (or down-path path) and a return path (or up-path) of the recording head scan in the main scanning direction.
But when the two-way recording is carried out, it is difficult to completely match the impact positions of the ink drops on the recording medium between the forward and return paths of the recording head, and a slight error occurs between the impact positions of the ink drops on the recording medium between the forward and return paths of the recording head. For this reason, when an attempt is made to simultaneously achieve a high-speed operation (or high-speed recording) and a high picture quality by simultaneously carrying out the interlace scanning and the two-way recording, the impact position error occurs for every other line (this impact position error will be referred to as a “two-way impact error”) and the picture quality greatly deteriorates as a result.
Japanese Laid-Open Patent Applications No. 11-48587 and No. 2004-288627 propose preventing the picture quality from becoming deteriorated by the above two-way impact error, by providing a pattern that can easily correct the impact positions before a user uses the recording apparatus, and enabling the user to carry out a correction operation based on this pattern.
A Japanese Laid-Open Patent Application No.2004-9333 proposes another method that records the dots with a priority in the forward path of the main scan, and filling the dots in the return path for gradation levels amounting to 50% or more of the recording density of the dots.
Furthermore, a Japanese Laid-Open Patent Application No.2004-166163 proposes a gradation reproducing method which carries out a halftone process using a dither matrix, by reproducing the gradation level by an inclined line-group keytone.
In the ink-jet recording apparatus, the gradation image may be formed by forming four kinds of dot sizes (large, medium, small and nil) by selectively ejecting ink with three kinds of ink drop sizes, namely, large ink drop, medium ink drop and small ink drop. But in this case, the extent of the two-way impact error becomes different depending on the ink drop sizes.
For example, if the recording head that ejects the ink uses a piezoelectric element, the kinetic energy of the ink drop, the air resistance the ink drop receives during flight and a driving signal waveform applied to the piezoelectric element to eject the ink drop respectively differ depending on the ink drop size. As a result, the amount of impact position error of the ink drop that is ejected from the recording head differs depending on the ink drop size. Moreover, if the nozzle diameters are made different in order to eject the ink with the different ink drop sizes, the amount of impact position error of the ink drop that is ejected from the recording head is also affected by the precision with which the recording head is made.
In other words, when carrying out the two-way recording by selectively ejecting the ink with the different ink drop sizes, it is extremely difficult to accurately match the impact positions of the ink drops for all ink drop sizes.
For this reason, there is a limit to suppressing the picture quality deterioration caused by the two-way impact error even if the methods proposed in the Japanese Laid-Open Patent Applications No.11-48587 and No.2004-188627 are employed. Accordingly, when generating the image data, the halftone process must be carried out under the precondition that the two-way impact error will occur, but this precondition was not take into consideration by the conventional methods.
On the other hand, although the Japanese Laid-Open Patent Application No.2004-9333 proposes a suitable method from the point of view of suppressing the picture quality deterioration caused by the two-way impact error, the dots formed by the small ink drops will be arranged linearly along the main scanning direction for every other line at the gradation level where the recording density of the small ink drops is 50%, for example. But such a dot arrangement is easily affected by inconsistencies in the sub scanning direction and inconsistencies in the ink ejection of the nozzles, and another problem is introduced in that a banding is easily generated.
The dither process based on the inclined line-group keytone as proposed in the Japanese Laid-Open Patent Application No.2004-166163 will not easily generate the banding. However, another problem is introduced in that a disorder of the inclined line-group keytone is generated if the two-way impact error occurs.